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气体动理学统一算法的隐式方法研究

毛枚良, 江定武, 李锦, 邓小刚

毛枚良, 江定武, 李锦, 邓小刚. 气体动理学统一算法的隐式方法研究[J]. 力学学报, 2015, 47(5): 822-829. DOI: 10.6052/0459-1879-14-408
引用本文: 毛枚良, 江定武, 李锦, 邓小刚. 气体动理学统一算法的隐式方法研究[J]. 力学学报, 2015, 47(5): 822-829. DOI: 10.6052/0459-1879-14-408
Mao Meiliang, Jiang Dingwu, Li Jin, Deng Xiaogang. STUDY ON IMPLICIT IMPLEMENTATION OF THE UNIFIED GAS KINETIC SCHEME[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 822-829. DOI: 10.6052/0459-1879-14-408
Citation: Mao Meiliang, Jiang Dingwu, Li Jin, Deng Xiaogang. STUDY ON IMPLICIT IMPLEMENTATION OF THE UNIFIED GAS KINETIC SCHEME[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 822-829. DOI: 10.6052/0459-1879-14-408
毛枚良, 江定武, 李锦, 邓小刚. 气体动理学统一算法的隐式方法研究[J]. 力学学报, 2015, 47(5): 822-829. CSTR: 32045.14.0459-1879-14-408
引用本文: 毛枚良, 江定武, 李锦, 邓小刚. 气体动理学统一算法的隐式方法研究[J]. 力学学报, 2015, 47(5): 822-829. CSTR: 32045.14.0459-1879-14-408
Mao Meiliang, Jiang Dingwu, Li Jin, Deng Xiaogang. STUDY ON IMPLICIT IMPLEMENTATION OF THE UNIFIED GAS KINETIC SCHEME[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 822-829. CSTR: 32045.14.0459-1879-14-408
Citation: Mao Meiliang, Jiang Dingwu, Li Jin, Deng Xiaogang. STUDY ON IMPLICIT IMPLEMENTATION OF THE UNIFIED GAS KINETIC SCHEME[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 822-829. CSTR: 32045.14.0459-1879-14-408

气体动理学统一算法的隐式方法研究

基金项目: 国家自然科学基金(11402287)、空气动力学国家重点实验室研究基金(SKLA2015-1-2)资助项目.
详细信息
    通讯作者:

    毛枚良,研究员,主要研究方向:复杂流动数值模拟方法及应用.E-mail:l219@163.com

  • 中图分类号: V211.3

STUDY ON IMPLICIT IMPLEMENTATION OF THE UNIFIED GAS KINETIC SCHEME

Funds: The project was supported by the National Natural Science Fundation of China(11402287) and Study Fund of State Key Laboratory of Aerodynamics (SKLA2015-1-2).
  • 摘要: 目前的气体动理学统一算法(unified gas kinetic scheme, 简称UGKS) 在求解高速流动问题时的计算效率,难以满足求解复杂工程问题的需求. 为了提高该算法的计算效率, 本文对模型方程的对流项和碰撞项进行了隐式处理, 并针对UGKS 界面通量与演化时间相关的特点, 引入了演化时间平均界面通量, 通过对控制方程矩阵进行近似LU 分解(lower-upper decomposition), 实现了隐式UGKS. 不同来流马赫数的圆柱绕流算例测试表明, 只要演化时间选取得当, 隐式方法可以得到与显式方法完全相同的结果, 且计算效率可以提高1~2 个量级.
    Abstract: The current explicit unified gas kinetic scheme (UGKS) is very time-consuming for high speed flows due to the massive phase space mesh demand, which is a bottleneck for complex engineering problems. In order to improve the efficiency, the motion and collision term in the model equation is implicitly treated and the evolving time averaged flux across the cell interface is introduced, then the implicit UGKS can be obtained applying the approximate LU decomposition on the matrix of the governing equations. The tests on the flows over a cylinder with different freestream Mach numbers show that the implicit method can give the same result as the original explicit method with a properly chosen evolving time step. Meanwhile, the computational efficiency can be improved by 1-2 orders.
  • Yu PB. A unied gas kinetic scheme for all knudsen number flows. [PhD Thesis], Hong Kong:The Hong Kong University of Science and Technology,2013.
    Chen SZ, Xu K, Lee CB, et al. A unified gas kinetic scheme with moving mesh and velocity space adaptation. Journal of Computational Physics, 2012, 231(20): 6643-6664.
    Arslanbekov RR, Kolobov VI, Kolobov AA. Kinetic solvers with adaptive mesh in phase space, In: Abe T, Ed. Rarefied Gas Dynamics, Melville, 2012, Amer Inst Physics, 2012, 294-301.
    Baranger C, Claudel J, Claudel N, et al. Locally refined discrete velocity grids for deterministic rarefied flow simulations, In: Abe T, Ed. Rarefied Gas Dynamics, Melville, 2012, Amer Inst Physics, 2012, 389-396.
    Yoon S, Jameson A. Lower upper symmetric Gauss Seidel method for the Euler and Navier-Stokes equations. AIAA Journal, 1988, 26(efeq9): 1025-1026.
    Yang JY, Huang JC. Rarefied flow computations using nonlinear model Boltzmann equations. Journal of Computational Physics, 1995, 120(efeq2): 323-339.
    毕林. Boltzmann模型方程数值算法在槽道流问题中的应用研究. [硕士论文].四川绵阳: 中国空气动力研究与发展中心, 2007 (Bi Lin. Application and study on numerical algorithm of the Boltzmann model equation in channel flow. [Master Thesis]. Mianyang: China Aerodynamic Research and Development Center, 2007 (in Chinese))
    王强, 程晓丽, 庄逢甘. 基于简化Boltzmann方程的超声速流稀薄效应分析. 航空学报, 2005. 26(efeq3):281-285 (Wang Qiang, Cheng Xiaoli, Zhuang Fenggan. Rarefaction effect analysis of supersonic flows based on reduced Boltzmann equations. Acta Aeronautica Et Astronautica Sinica, 2005, 26(efeq3): 281-285 (in Chinese))
    王强, 程晓丽, 庄逢甘. 稀薄流非线性模型方程离散速度坐标法有限差分解. 计算力学学报, 2006, 23(efeq2): 235-241 (Wang Qiang, Cheng Xiaoli, Zhuang Fenggan. Finite difference solution of nonlinear model equations for rarified gas using discrete velocity ordinate method. Chinese Journal of Computational Mechanics, 2006, 23(efeq2): 235-241 (in Chinese))
    Titarev VA. Efficient deterministic modelling of three-dimensional rarefied gas flows. Communications in Computational Physics, 2012, 12(efeq1):162-192.
    Titarev VA, Dumbser M, Utyuzhnikov S. Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions. Journal of Computational Physics, 2014, 256: 17-33.
    Xu K, Huang JC. A unified gas-kinetic scheme for continuum and rarefied flows. Journal of Computational Physics, 2010, 229(20): 7747-7764.
    Huang JC, Xu K, Yu PB. A unified gas-kinetic scheme for continuum and rarefied flows II: multi-dimensional cases. Communications in Computational Physics, 2012, 12(efeq3): 662-690.
    Huang JC, Xu K, Yu PB. A unified gas-kinetic scheme for continuum and rarefied flows III: Microflow simulations. Communications in Computational Physics, 2012, 14(efeq5): 1147-1173.
    徐昆, 李启兵, 黎作武. 离散空间直接建模的计算流体力学方法. 中国科学: 物理学 力学 天文学, 2014, 44(efeq5):519-530 (Xu Kun, Li Qibing, Li Zuowu. Direct modeling-based computational fluid dynamics. Scientia Sinica Physica, Mechanica & Astronomica, 2014, 44(efeq5): 519-530 (in Chinese))
    Xu K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. Journal of Computational Physics, 2001, 171(efeq1): 289-335.
    毛枚良, 徐昆, 邓小刚. 动能BGK算法在近连续流模拟中的应用. 空气动力学学报, 2005, 23(efeq3): 317-321 (Mao Meiliang, Xu Kun, Deng Xiaogang. Application of kinetic BGK algorithm in simulating near continuum flow. Acta Aerodynamica Sinica, 2005, 23(efeq3): 317-321 (in Chinese))
    Xu K, Mao ML, Tang L. A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow. Journal of Computational Physics, 2005, 203(efeq2): 405-421.
    Jiang J, Qian YH. Implicit gas-kinetic BGK scheme with multigrid for 3D stationary transonic high-Reynolds number flows. Computers & Fluids, 2012, 66: 21-28.
    Li WD, Masayuki K, Kazuhiko S. An implicit gas kinetic BGK scheme for high temperature equilibrium gas flows on unstructured meshes. Computers & Fluids, 2014, 93: 100-106.
    Jiang DW, Li J, Mao ML, et al. Implicit implementation of bgk-ns method and its application in complex flows. Transactions of Nanjing University of Aeronautics & Astronautics, 2013, 30(supp): 87-92.
    Bird GA. The DS2V/3V program suite for DSMC calculations, In: Capitelli M, Ed. Rarefied Gas Dynamics, 2005, Amer Inst Physics, 2005, 541-546.
    Shakhov E. Generalization of the Krook kinetic equation. Fluid Dynamics, 1968, 3(efeq5): 95-96.
    江定武, 毛枚良, 李锦 等. 气体动理学统一算法中相容性条件不满足引起的数值误差及其影响研究. 力学学报, 2014, 47(efeq1): 163-168 (Jiang Dingwu, Mao Meiliang, Li Jin, et al. Study on the numerical error introduced by dissatisfying the conservation constraint in UGKS and its effects. Chinese Journal of Theoretical and Applied Mechanics, 2014, 47(efeq1): 163-168 (in Chinese))
    Liu HL, Cai CP, Zou C. An object-oriented serial implementation of a DSMC simulation package. Computers & Fluids, 2012, 57: 66-75.
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  • 被引次数: 16
出版历程
  • 收稿日期:  2014-12-18
  • 修回日期:  2015-06-05
  • 刊出日期:  2015-09-17

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